Neural graph matching.
Following recent progress in neural graph matching [1]}, [2]}, we
incorporate message passing within a graph (called intra-graph message)
and between a pair of graphs (called inter-graph messages).
Given a intra-graph node pair \(\langle s, t\rangle \)  and a inter-graph node pair \(\langle s^{\prime }, t^{\prime }\rangle \) , we define the two kinds of message passing mechanisms formally as:
\(\mathbf {m}_{s \rightarrow t}&= \operatorname{MSG}_{\operatorname{intra}}\left(\mathbf {h}_{s}^{(1)}, \mathbf {h}_{t}^{(1)}, \mathbf {e}_{s t}\right), \\\mathbf {\mu }_{s^{\prime } \rightarrow t^{\prime }}&= \operatorname{MSG}_{\operatorname{inter}}\left(\mathbf {h}_{s^{\prime }}^{(1)}, \mathbf {h}_{t^{\prime }}^{(2)}\right),\) 
